Duality of positive and negative integrable hierarchies via relativistically invariant fields

doi:10.1007/JHEP07(2021)058

	Duality of positive and negative integrable hierarchies via relativistically invariant fields
	Lou, S. Y.4; Hu, X. B.2,3; Liu, Q. P.1
刊名	JOURNAL OF HIGH ENERGY PHYSICS
	2021-07-12
期号	7 页码:22
关键词	Integrable Hierarchies Integrable Field Theories Space-Time Symmetries
ISSN号	1029-8479
DOI	10.1007/JHEP07(2021)058
英文摘要	It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some continuous and discrete integrable positive hierarchies such as the potential modified Korteweg-de Vries hierarchy, the potential Fordy-Gibbons hierarchies, the potential dispersionless Kadomtsev-Petviashvili-like (dKPL) hierarchy, the differential-difference dKPL hierarchy and the second heavenly hierarchies are converted to the integrable negative hierarchies including the sG hierarchy and the Tzitzeica hierarchy, the two-dimensional dispersionless Toda hierarchy, the two-dimensional Toda hierarchies and negative heavenly hierarchy. In (1+1)-dimensional cases the positive/negative hierarchy dualities are guaranteed by the dualities between the recursion operators and their inverses. In (2+1)-dimensional cases, the positive/negative hierarchy dualities are explicitly shown by using the formal series symmetry approach, the mastersymmetry method and the relativistic invariance of the duality relations. For the 4-dimensional heavenly system, the duality problem is studied firstly by formal series symmetry approach. Two elegant commuting recursion operators of the heavenly equation appear naturally from the formal series symmetry approach so that the duality problem can also be studied by means of the recursion operators.
资助项目	National Natural Science Foundations of China[11975131] ; National Natural Science Foundations of China[11871471] ; National Natural Science Foundations of China[11931017] ; K. C. Wong Magna Fund in Ningbo University
WOS研究方向	Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000675383900002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58959]
专题	中国科学院数学与系统科学研究院
通讯作者	Lou, S. Y.
作者单位	1.China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 4.Ningbo Univ, Sch Phys Sci & Technol, Ningbo 315211, Peoples R China
推荐引用方式 GB/T 7714	Lou, S. Y.,Hu, X. B.,Liu, Q. P.. Duality of positive and negative integrable hierarchies via relativistically invariant fields[J]. JOURNAL OF HIGH ENERGY PHYSICS,2021(7):22.
APA	Lou, S. Y.,Hu, X. B.,&Liu, Q. P..(2021).Duality of positive and negative integrable hierarchies via relativistically invariant fields.JOURNAL OF HIGH ENERGY PHYSICS(7),22.
MLA	Lou, S. Y.,et al."Duality of positive and negative integrable hierarchies via relativistically invariant fields".JOURNAL OF HIGH ENERGY PHYSICS .7(2021):22.